SLAC-PUB-6662 September 1994 (Ml TESTING SUPERSYMMETRY AT THE NEXT LINEAR COLLIDER JONATHAN L. FENG * Stanford Linear Accelerator Center Stanford University, Stanford, California 94309 and Physics Department Stanford University, Stanford, California 94305 ABSTRACT If new particles are discovered, it will be important to determine if they are the supersymmetric partners of standard model bosons and fermions. Super- symmetry predicts relations among the couplings and masses of these particles. We discuss the prospects for testing these relations at a future e+e- linear col- lider with measurements that exploit the availability of polarized beams. Talk presented at DPF’94: Eighth Meeting of the Division of Particles and Fields of the American Physical Society Albuquerque, New Mexico, August 2-6, 1994 *Work supported by the Department of Energy, contract DE-AC03-76SF00515, and in part by an NSF Graduate Research Fellowship. - _-, - -a-- -- 9 . 1 1. Introduction The phenomenological predictions of supersymmetry (SUSY) may be divided into the following three categories: (I) predictions that would -constitute indirect evidence for SUSY if verified, including, for example, the existence of a light Higgs bosom (II) the existence of particles with the correct spin and quantum numbers to be superpartners -- of standard model particles; and (III) well-defined quantitative relations among the couplingsand masses of these new particles. While the predictions of (I) are of great interest, their verification is clearly no substitute for direct evidence. The discovery of a large number of particles in category (II) would be strong support for SUSY, but it is unlikely that future searches will immediately yield many sparticles. On the other hand, if only one or a few new particles are discovered, precise verification of the relations of category (III) could be taken as confirmation of SUSY. It is the prospects for such tests that we investigate in this study. Studies have shown that the Next Linear Collider, a proposed linear e+e- collider with fi = 500 GeV and a luminosity of 10 - lOOfb-‘/year, is a powerful tool for -- I studying the properties of new partic1es.l The clean environment and polarizable beams provided by such a machine make it well-suited to precision studies, and we will study the prospects for precision tests of SUSY in this setting. We will also limit the discussion to the case in which charginos are produced, but slepton and squark pair production - _ - is beyond reach. Remarks about other scenarios may be found in an extended version of this work done with H. Murayama, M. E. Peskin, and X. Tata. In Sec. 2 we assume SUSY and use it as a guide to selecting well-motivated case studies. We review the parameters that enter chargino production and decay, and we divide the SUSY parameter space into characteristic regions. In Sec. 3 we explore the first of these regions and test the form of the chargino mass matrix. In Sec. 4 we consider another region and test the chargino-fermion-sfermion coupling. 2. Regions of Parameter Space 1 This study will be conducted in the context of the minimal supersymmetric stan- dard model (MSSM), th e sup&symmetric extension of the standard model with min- imal field content. The charginos of the MSSM are mixtures of the charged Higgsinos - - 2 and electroweak gauginos and have mass terms ($J-)~M~*$+ + h.c., where JJ2 fiMwsinp fiMwcos/3 p ’ (1) and ($*)’ = (-;l@*,fi*). Th e chargino mass eigenstates are 2: = xj$f and 2; = U;j$j. The matrices V and U are effectively orthogonal rotation matrices parametrized by the angles ++ and $-, respectively. We assume that R-parity is conserved, the LSP is the lightest neutralino Xy, there is no intergenerational mixing in the sfermion sector, and sleptons and squarks are degenerate with masses mi and rnd, respectively. (The last assumption may be partially relaxed.3) With these assumptions, the parameters that enter chargino events are p, M2, tanp, nil,, ml, and m,-. With an ei beam, chargino production occurs through s-channel 2 and y diagrams and t-channel ce exchange, and so daL/d cos 8 is governed by the first four parameters. In the case of an ek beam, the Y, diagram is absent, and so daR/d cos B is dependent on only the first three parameters CL, M2, and tan ,B. Charginos decay to the LSP either leptonically through W bosons or virtual sleptons, g+ --+ (X%V+, l;v, lfi*) -+ X~?V, or hadronically through IV bosons or virtual squarks, g+ t (gTW+, Q”*q’,&‘*) + ,gQq’. All six parameters enter the decay process. We now divide the parameter space into characteristic regions. The chargino - masses and 0~ E g(eRei -+ X:X,) depend only on p, M2, and tan /?. The dependence on tan p is wea-k; we set tan ,B = 4 as a representative case. In Fig. 1, the cross-hatched region is excluded by present experiments, and chargino production is inaccessible for fi = 50dGeV in the hatched region. We divide the remaining bands of the (p, M2) plane into the three regions indicated. In region 1, XFjjr production is possible, and so both chargino masses can be measured. Where 2: is inaccessible, OR distinguishes regions 2 (shaded, OR M 0) and 3 (where, typically, 0~ > 50 fb). We will consider case studies in which rnlif M 170 GeV; this contour is the dotted curve in Fig. 1. Region 3 presents difficulties even for the identification of a SUSY signal, since the 2: and 2: become degenerate as M2 increases. Although it may be possible to verify SUSY relations in certain parts of region 3, we will not consider this case further. 3 600 -600 -300 0 300 600 9-94 779OAl CL WV) Fig. 1. The characteristic regions of parameter space. 3. Region 1 In region 1 we take the representative point in parameter space to be (cl, n/r,, tan p, Ml/Mx, mi, mi) = (-195,210,4, 0.5,400, 700). For these parameters, rng: = 172 GeV, mxy = 105GeV, and rn%; = 255GeV. The uncertainty in determining these masses is very small’ and will be unimportant for this study. There are additional features that are typical of Region 1: OR is large enough to yield many events for study, and 2: 25 iif , so the leptonic branching fraction Bl is i to a very good approximation. In this region we generalize the chargino mass matrix to an arbitrary real 2 x 2 matrix, which we parametrize as fiM$, sin/? (2) &?M~cos/~ p - Our goal is to test the SUSY relation M$, = Mw, that is, the equality of the Higgs boson and Higgsino couplings. Formally, this is a simple task. The four parameters en- tering Eq. 2 may be exchanged for the parameters m%:, rn?;, $+ and d-. By measuring mn~, ma;, and two quantities derived from daR/d cos 0, we may restrict the variables (4+, $-) and may therefore bound M$. It is useful to work with the total cross section OR and a truncated forward-backward asymmetry AgB, defined below. Unfortunately, neither quantity is observed directly. We have performed Monte Carlo simulations at a large number of points obtained by varying the supersymmetry parameters and M$ to determine the correlation of these quantities to experimental observables. The Monte Carlo simulations for chargino events used the parton-level event generator of Feng and Strassler3 with detector parameters as chosen in the JLC study.’ Chargino events were selected from mixed-mode events in which one chargino decays hadronically and the other leptonically, using the system of cuts presented by the JLC group. These cuts include the elimination of events with very forward leptons or hadron jets (cos ohad, cos& < 0.75), t o remove the forward peak of WW events. With these cuts and a highly polarized eE beam, the total background is negligible. To find OR, we use the event rate in the mixed mode, the leptonic branching ratio Bl = f, and the efficiency of the cuts determined by Monte Carlo. The simulations also tell us that the theoretical quantity aX(O < cos 0 < 0.75) - 0x(-l < cos 0 < 0) A& E 0X(-l < cos 0 < 0.75) (3) is highly correlated with the forward-backward asymmetry of the hadronic system’s direction. For an integrated luminosity of 50 fb-I, these two quantities should be de- termined to the level CR = 48 f 2.4 fb, AgB = -37 f 6.9%, where the la errors include uncertainty from the variation of parameters. The measurements of AgB and OR constrain the ($+, $-) pl ane to the shaded region in Fig. 2. In this allowed region, 65 GeV < M& < 100 GeV, a significant quantitative confirmation of SUSY. 5 0 30 60 90 9-94 779OA3 $+ wwes) Fig. 2. The allowed region of the (4+,4-) pl ane. Contours of M& are plotted in GeV. 4. Region 2 In region 2 we take the representative point to be (p, M2, tan ,B, M,/Mz, my, m,-) = - (-500,170,4,0.5,400,700). For these parameters, rng; = 172 GeV, rnxy = 86GeV, rnx; = 512GeT(, and aR M 0. Here we must rely on measurement of dgL/d cos 0, which introduces dependence on mp. Fortunately, there is a compensating simplification: in region 2, $+, $- M 0, i.e., charginos and neutralinos are very nearly pure gauginos. In addition, as is typical in region 2, on-shell W decays are allowed, and so again Bl = 5. We will generalize the ifff coupling to gXVll and test the SUSY relation gx = g, that is the equality of the W boson and wino couplings. The differential cross section dgL/d cos 8 is a function of (rn%;, d+, $-, my, gx), but because we can measure rn?;, and $+, 4- M 0, we have only two unknowns.